Query Asst 6

course Phy 122

ՠgalassignment #006

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006.

Physics II

06-08-2007

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12:09:43

Query Principles and General Physics 17.4: work by field on proton from potential +135 V to potential -55 V.

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RESPONSE -->

This exact problem is not in my book. It is very similar to 17.2, which reads:

""How much work does the electric field do in moving a proton from a point with a potential of +125V to a point where is is

-55V? Express your answer both in joules and electron volts.""

In this case, we set the change in potential energy equal to the work required of an external force:

W = `dPE = q(Vb - Va) = (1.6*10^-19C)(-55V - 125V) = -2.88*10^-17 J

The electron volts of the proton will be 180V*1e = 180eV.

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12:10:52

The change in potential is final potential - initial potential = -55 V - (125 V) = -180 V, so the change in the potential

energy of the proton is {}{}-180 V * 1.6 * 10^-19 C ={}-180 J / C * 1.6 * 10^-19 C = -2.9 * 10^-17 J. {}{}In the absence of

dissipative forces this is equal and opposite to the change in the KE of the proton; i.e., the proton would gain 2.9 * 10^-17

J of kinetic energy.{}{} Change in potential energy is equal and opposite to the work done by the field on the charge, so the

field does 2.9 * 10^-17 J of work on the charge.{}{}Since the charge of the proton is equal in magnitude to that of an

electron, he work in electron volts would be 180 volts * charge of 1 electron= 180 eV.

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RESPONSE -->

I feel that I adequately answered this problem. However, I did not mention that in the absence of dissipative forces the work

is equal and opposite to the change in kinetic energy.

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12:15:14

Query Principles and General Physics 17.8: Potential difference required to give He nucleus 65.0 keV of KE.

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RESPONSE -->

We are told that the charge of the He nucleus is Q = 2e

65.0 keV = 6.5*10^4 eV

If the nucleus receives 2e of KE for every unit of voltage, then to reach 65 kev the nucleus would need half of that value.

6.5*10^4 eV/ 2e = 3.25*10^4 V

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12:18:34

65.0 keV is 65.0 * 10^3 eV, or 6.50 * 10^4 eV, of energy. {}{}The charge on a He nucleus is +2 e, where e is the charge on

an electron. So assuming no dissipative forces, for every volt of potential difference, the He nuclues would gain 2 eV of

kinetic energy.{}{}To gain 6.50 * 10^4 eV of energy the voltage difference would therefore be half of 6.50 * 10^4 voles, or

3.35 * 10^4 volts.

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RESPONSE -->

My answer was slightly different, 3.25*10^4 V.

I believe your answer is correct; my error was (hopefully) a typo.

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12:18:44

Query gen phy text problem 17.18 potential 2.5 * 10^-15 m from proton; PE of two protons at this separation in a nucleus.

What is the electrostatic potential at a distance of 2.5 * 10^-15 meters?

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RESPONSE -->

I am not a general physics student, but I would like to try to answer this question.

a)Electric potential can be found by the equation V = kQ/r, where Q would be the charge of the proton (same magnitude as an

electron) and r is the distance to the proton, 2.5*10^-15m.

V = [(9*10^9 Nm^2/C^2)(1.6*10^-19C)]/(2.5*10^-15m) = 5.76*10^5 V

b) I don't know how to complete this part.

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12:19:18

STUDENT SOLUTION: For a part, to determine the electric potential a distance fo 2.5810^-15m away from a proton, I simply

used the equation V = k q / r for electric potential for point charge:

q = 1.60*10^-19C=charge on proton

V = kq/r = 9.0*10^9N*m^2/C^2(1.60*10^-19C) / (2.5*10^-15m) = 5.8*10^5V.

Part B was the more difficult portion of the problem. You have to consider a system that consists of two protons 2.5*10^-5m

apart.

The work done against the electric field to assemble these charges is W = qV. The potential energy is equal to the work done

against the field.

PE=(1.60*10^-19C)(5.8*10^5V)

= 9.2*10^-14 J.

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RESPONSE -->

I have read the solution, but I don't quite understand what this student did in part B. I know that this question wasn't

meant for my section, but I would like to know how to do it.

Change in voltage between two points is equal to the work done against the electric field, per unit of charge, to move between those points. This is equal to the change in electrostatic potential energy between the points, per unit of charge.

Change in voltage, work done against electric field per unit of charge, and change in electrostatic potential energy per unit of charge are all measured in Joules / Coulomb.

To assemble the system of charges, we start with the charges far apart and bring them to the given proximity.

When far apart, the force between the charges is essentially zero (the term 'far apart' implies a distance great enough that the force is negligible). As the two protons approach one another they exert a mutually repulsive force, which increases in proportion to the inverse square of their separation. The work done over any small interval is equal to the average force exerted for that interval, times the change in the separation of the charges.

We could approximate this work by breaking the change in separation into small intervals, over each of which the change in force is insignificant. Summing the force * difference in separation over all such intervals we would arrive at a good approximation to the total work done.

Using techniques of calculus (specifically, for those who know some integral calculus, we integrate the force function F = k q1 q2 / r^2 with respect to separation r) we find that the work required to assemble the charges at separation r, starting from distant initial separation, is k q1 q2 / r.

This work is done against the conservative electrostatic force between the charges. Change in PE is equal to the work done against conservative forces. So the electrostatic PE at separation r is k q1 q2 / r, relative to large separation (considered to be infinite separation--you don't have to get too far apart before the difference between large separation and infinite separation is negligible).

If we want to find the voltage, or electrostatic potential, of charge q2 at separation r, that is just the PE per unit of charge, or PE / q2. This is (k q1 q2 / r) / q2 = k q1 / r.

If q1 is the charge of 'the other' proton, then this expression gives the electrostatic potential at distance r. For the given separation r, this is 5.76 * 10^5 V, or 5.76 * 10^5 J / C.

Multiplying by the charge of the second proton gives the electrostatic potential energy at distance r, which is 9.2 * 10^-14 J. This is, for the reasons given above, the work required to assemble this system.

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12:19:36

query univ phy 23.58 (24.58 10th edition). Geiger counter: long central wire 145 microns radius, hollow cylinder radius 1.8

cm.

What potential difference between the wire in the cylinder will produce an electric field of 20,000 volts/m at 1.2 cm from

the wire?

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RESPONSE -->

I am not a university of physics student

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12:19:49

** The voltage V_ab is obtained by integrating the electric field from the radius of the central wire to the outer radius.

From this we determine that E = Vab / ln(b/a) * 1/r, where a is the inner radius and b the outer radius.

If E = 20,000 V/m at r = 1.2 cm then

Vab = E * r * ln(b/a) = 20,000 V/m * ln(1.8 cm / .0145 cm) * .012 m = 1157 V. **

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RESPONSE -->

ok

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12:20:01

Query univ 23.78 (24.72 10th edition). Rain drop radius .65 mm charge -1.2 pC.

What is the potential at the surface of the rain drop?

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RESPONSE -->

I am not a university of physics student

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12:20:40

STUDENT RESPONSE FOLLOWED BY SOLUTION: The problem said that V was 0 at d = inifinity, which I understnad to mean that as we

approach the raindrop from infinity, the potential differencegrows from 0, to some amount at the surface of the raindrop.

Because water molecules are more positive on one side that the other, they tend to align in a certain direction. Since

positive charges tend to drift toward negative charge, I would think that the raindrop, with its overall negative charge, has

molecules arranged so that their more positive sides are pointing toward the center and negative sides will be alighed along

the surface of the raindrop. Probably all wrong. I tried several differnet integrand configuraitons but never found one

that gave me an answer in volts.

SOLUTION:

You will have charge Q = -1.2 * 10^-12 C on the surface of a sphere of radius .00065 m.

The field is therefore E = k Q / r^2 = 9 * 10^9 N m^2 / C^2 * (-1.2 * 10^-12 C) / r^2 = -1.08 * 10^-2 N m^2 / C / r^2.

Integrating the field from infinity to .00065 m we get

(-1.08 * 10^-2 N m^2 / C) / (.00065 m) = -16.6 N m / C = -16.6 V.

If two such drops merge they form a sphere with twice the volume and hence 2^(1/3) times the radius, and twice the charge.

The surface potential is proportional to charge and inversely proportional to volume. So the surface potential will be 2 /

2^(1/3) = 2^(2/3) times as great as before.

The surface potential is therefore 16.6 V * 2^(2/3) = -26.4 volts, approx.. **

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RESPONSE -->

ok

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This looks very good. Let me know if you have any questions. &#